1.

If

Answer»
  • ∠BCD is of 100°.

Step-by-step explanation:

Given

  • ∠ABD is 70°
  • ∠ADB is 30°.

To FIND:-

  • Measure of ∠BCD

Solution:-

We know that,

Sum of all interior angles of triangle is 180°. This PROPERTY is also KNOWN as'Angle sum property of TRIANGLE'.

So,

➞ ∠A + ∠ABD + ∠ADB = 180°

➞ ∠A + 70° + 30° = 180°

➞ ∠A + 100° = 180°

➞ ∠A = 180° - 100°

➞ ∠A = 80°

  • Given QUADRILATERAL is cyclic quadrilateral because it's all vertices are lying on the circumference of circle.

We also know that,

Sum of any two opposite angles of any cyclic quadrilateral is 180°.

So,

➞ ∠A + ∠BCD = 180°

➞ 80° + ∠BCD = 180°

➞ ∠BCD = 180° - 80°

➞ ∠BCD = 100°.

Therefore,

∠BCD is of 100°.


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